As a method for producing a cis-3-substituted-3-azabicyclo[3.2.1]octan-8-ol derivative, for example, a method wherein 3-methyl-3-azabicyclo[3.2.1]octan-8-one is reduced with metal sodium, and heated for 230 hours in the presence of benzophenone (see Non-Patent Document 1) is known.
Further, the following method is known in which 3-methyl-3-azabicyclo[3.2.1]octan-8-one is reduced normally to obtain a trans, and transformed into triflate, and then, inversed with acid (see Non-Patent Document 2).
Meanwhile, a racemization reaction of optically active alcohol using a ruthenium complex as a catalyst is known (see Non-Patent Documents 3 and 4).    Non-Patent Reference 1: J. Org. Chem., 1963, 28, 2407    Non-Patent Reference 2: J. Med. Chem., 2003, 46, 1456    Non-Patent Reference 3: J. Organomet., Chem., 2002, 652, 105    Non-Patent Reference 4: Tetrahedron Lett., 2003, 44, 7521